How to slove this question?

Consider a matrix A with the special property that A"/ = Z for some integer m. Here Z is the zero-matrix (i.e. the matrix filled with zeroes). Such a matrix A is called nilpotent, and as it is clearly special, it will have special eigenvalues. Say v is an eigenvector of A with eigenvalue t. By left-multiplying m times by the matrix A we get Amv = Zv =0. Since v is an eigenvector with eigenvalue t, this implies that tmv = 0. Since eigenvectors are non-zero |the only way this can be satisfied is if t'm = 0, implying that the eigenvalues of A must be zero An example of a nilpotent matrix is B = 0 0 0 0 0 since Bill = 0 0 0 where m = 0 0